Block #458,428

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/24/2014, 2:16:50 PM · Difficulty 10.4207 · 6,349,370 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

d0c36e9b1f814c8b8c167fef0f776fefed62650d652dd9548762d7960e598b36

View on Chainz ↗

Height

#458,428

Difficulty

10.420742

Transactions

Size

900 B

Version

Bits

0a6bb5c5

Nonce

46,466

Timestamp

3/24/2014, 2:16:50 PM

Confirmations

6,349,370

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

53b70d698d4f42fc204e03944e04d15f5bcd17d6a4f20252ead76f75c0ea80b6

Transactions (1)

Coinbase53b70d698d4f42…d76f75c0ea80b6

1 in → 22 out9.1900 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AbPcCMg4…719q6mAX AUzEPJFG…kYkA5U9V

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.119 × 10⁹¹(92-digit number)

21192311660542952961…25594204006219018079

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

2.119 × 10⁹¹(92-digit number)

21192311660542952961…25594204006219018079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.238 × 10⁹¹(92-digit number)

42384623321085905923…51188408012438036159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.476 × 10⁹¹(92-digit number)

84769246642171811847…02376816024876072319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.695 × 10⁹²(93-digit number)

16953849328434362369…04753632049752144639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.390 × 10⁹²(93-digit number)

33907698656868724739…09507264099504289279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.781 × 10⁹²(93-digit number)

67815397313737449478…19014528199008578559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.356 × 10⁹³(94-digit number)

13563079462747489895…38029056398017157119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.712 × 10⁹³(94-digit number)

27126158925494979791…76058112796034314239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.425 × 10⁹³(94-digit number)

54252317850989959582…52116225592068628479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.085 × 10⁹⁴(95-digit number)

10850463570197991916…04232451184137256959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #458,428

Cookie Preferences